Front derailer not responding

Rookie mechanic here...

I have a 2010 Trek 1.1 C road bike (58) that is less than one year old. From day one I've had a consistent problem -- the chain rubs the front derailer and makes lots of noise when I shift to gears 6, 7 or 8 on the rear cassette. I could tell the noise was coming from the chain rubbing the front derailer just by watching/listening with the bike on a rack.

What I did about it:
1. With the chain shifted onto the largest front chain ring I cranked the pedals and confirmed visually that the chain begins to rub when I shift to 6, 7 and 8 on the rear cassette. I did.
2. I adjusted the L screw on the front derailer to bring it outward a bit so it was just barely not touching the chain anymore, then shifted to 7 and 8 and observed no more rubbing or noise.
3. I pedaledt he bike around my neighborhood for several minutes and shifted constantly through all 8 gears leaving the front on 2. No problems or noise.

Now the front derailer does not respond when I try to shift onto the smaller chainring. I see the cable go totally limp, practically flapping in the wind underneath the down tube. The derailer doesn't move.

One possibility is that the derailleur's return spring is broken. Does it move back and forth with no spring resistance if you actuate it by hand?

Regarding the original problem, your shifter has a trim click to move the cage over enough to eliminate that rubbing. The chain may rub on the side of the big chainring in the cross-chained position, which is your signal to "hey, shift up to the big ring already."

This should have been sorted when you purchased the bike, the Front mech is an easy part of the bike to get right.

As noted by mechBgon, there will be some rubbing when the chain is crossed, but this just tessly you to shift.

If you follow the tech doc instructions, they show how to correctly set up the derailler. As the bike is a year old, it may be worth replacing the cables first, as these may have some strech in them before looking at changing the derailer

You monkeyed with the "L" adjustment on the big ring? That may be your problem. Try the "H" to get the big ring limit, and "L" to get the small ring limit right. After that, it's cable tension (assuming your derailleur is in the right place).

1) The limit screw is preventing the derailleur cage from moving as far as it should.
2) Normal rub caused by the chain's movement from shifting the rear. Solution is to "trim" or "microshift" the front just enough to stop the rubbing while riding.

Perhaps you adjusted the limit screw too much, when you actually just need to trim while riding (#2).

Yes it actuates by hand just fine. I was told just recently that I should have tried tightening the cable first instead of adjusting the hi/low positions on the deraillleur. I think when I adjusted the L screw I took it far enough that the cable literally cannot move it to the point associated with kicking onto the low gear.